Aggregate Effects in Local Labor Markets of Supply and Demand Shocks

Upjohn Institute Working Papers Upjohn Research home page 1999 Aggregate Effects in Local Labor Markets of Supply and Demand Shocks Timothy J. Bartik W.E. Upjohn Institute, bartik@upjohn.org Upjohn Institute Working Paper No. 99-57 **Published Version** Journal of Regional Science 42(4) (November 2002): 667-701 under title Spillover Effects of Welfare Reforms in State Labor Markets Citation Bartik, Timothy J. 1999. "Aggregate Effects in Local Labor Markets of Supply and Demand Shocks." Upjohn Institute Working Paper No. 99-57. Kalamazoo, MI: W.E. Upjohn Institute for Employment Research. https://doi.org/10.17848/wp99-57 This title is brought to you by the Upjohn Institute. For more information, please contact ir@upjohn.org.

Aggregate Effects in Local Labor Markets of Supply and Demand Shocks Upjohn Institute Staff Working Paper No. 99-57 by Timothy J. Bartik Senior Economist The W. E. Upjohn Institute for Employment Research 300 S. Westnedge Avenue Kalamazoo, MI 49007-4686 July 1999 I greatly appreciate the research assistance of Ken Kline, the editorial assistance of David Nadziejka, and the secretarial assistance of Claire Black. They went well beyond the call of duty with this complex project. This project was financially supported by the Upjohn Institute, the Russell Sage Foundation, and the Rockefeller Foundation. The findings and conclusions of this paper are those of the author, and may not reflect the views of any of the project s sponsors.

Aggregate Effects in Local Labor Markets of Supply and Demand Shocks Abstract Anti-poverty policy in the U.S. has emphasized labor supply policies, such as welfare reform or job training. Anti-poverty policy in the U.S. has not emphasized policies to increase labor demand for the poor, such as public employment or subsidizing private employers to hire the poor. What are the aggregate effects of such policies on wages and unemployment of different groups? This paper estimates and simulates a model with several types of labor, using data from the Current Population Survey on state labor markets. The simulations suggest that forcing more disadvantaged persons into the labor market can displace many other persons from employment in the short-run and medium-run, and increased public employment of the poor may be offset by reduced private employment of the poor in the long run. Wage subsidies to either the poor or the poor s employers have little effect on the poor s employment or market wages, although paying wage subsidies to the poor increases take-home pay. Finally education policies not only directly help those educated, but also increase average earnings of less-educated groups and reduce average earnings of more-educated groups.

1 We suspect that macro effects [of a social policy change] are often substantial, and that, correspondingly, the policy impacts determined by micro-experimental evaluations are often seriously biased... [T]he only way to determine the magnitude of macro effects is to measure them, something that has not been done. Irwin Garfinkel, Charles F. Manski, and Charles Michalopoulos, Micro Experiments and Macro Effects (p.254), in Evaluating Welfare and Training Programs (Eds., Charles F. Manski and Irwin Garfinkel), Harvard University Press, 1992. 1. Introduction How can policymakers best increase employment or wages of the poor? In the U.S., antipoverty policies devote more resources to labor supply policies than labor demand policies. Labor supply policies, which increase the quantity or quality of the poor s labor supply, include welfare-to-work programs, job training, and education. Labor demand policies, which increase demand for the poor s labor, include public employment and wage subsidies. The relative merits of labor supply vs. demand policies depend in part on their aggregate labor market effects. For example, job training for the poor is less attractive if every job gained by a trainee displaces someone else from a job. As noted by Garfinkel et al. in the above quotation, almost no studies have estimated these aggregate or macro effects. The present paper provides estimates of the aggregate effects of both labor supply and demand policies. These estimates of aggregate effects use a structural model of the labor market, which describes the labor supply and demand of different groups and their relationship to labor market outcomes. The structural model allows for involuntary unemployment. The model is estimated using pooled time-series cross-section data, with annual observations on average values of different labor market variables for 50 states and the District of Columbia, from 1979 to 1997. The model s data are derived from the Current Population Survey Outgoing Rotation Group (CPS-ORG). The model considers five groups: men and women, each divided into a less- and a

2 more-educated group, and with less-educated women divided into a less-educated single mother group and the remainder of less-educated women. Preliminary simulations examine the behavior of different parts of the model, including elasticities of labor supply and labor demand. Other simulations examine how wages, employment, and other labor market variables respond to labor supply and demand shocks. The shocks considered include quantity shocks to the labor supply or demand of each group and wage subsidy shocks to the demand or supply of each group. I also consider education shocks that switch labor supply from one group to another, and demand-shift shocks that switch labor demand towards more-educated groups. The most important implication of these simulations is that the aggregate effects of labor market policies are large. A labor market policy targeted on one group often has spillover effects on other groups of comparable magnitude to the direct effects of the policy on the targeted group. 2. Theory of Wage and Displacement Effects of Labor Supply and Demand Shocks Figure 1 illustrates the wage and displacement effects of shocks to labor supply and demand. The diagrams show a labor market, which could be the entire labor market or the market for some type of labor. Shocks will affect wages for all workers, not just workers who participate in some program. Market wages decrease due to supply shocks and increase due to demand shocks. For shocks to the quantity supplied or demanded, the increase in employment is less than the number of workers added to the market or employed by the policy, because some workers are displaced by program participants. For wage subsidies, the wage received by workers goes up by less than the amount of the subsidy.

3 Quantity Shock Figure 1A. Effects of a Labor Supply Shock Wage LD LS 1 LS W0 W1 Sq = workers added to labor market Wage Shock LD Wage (E1 - Sq) E0 E1 LS Employment 1 LS W1 + Sp W0 W1 Wage subsidy to workers is Sp E0 E1 Employment

4 Quantity Shock Figure 1B. Effects of a Labor Demand Shock Wage LD 1 LD LS W1 Dq = workers hired by program W0 Wage Shock (E1 - Dq) E0 E1 Employment LS Wage 1 LD LD W1 Dp = wage subsidy to employers W0 W1 - Dp E0 E1 Employment

5 It is apparent from Figure 1 that wage and displacement effects depend on the slopes of supply and demand curves. One can derive the following formulas 1 for the wage and employment effects of demand and supply shocks: (1) %)W = [d q + 0d p - s q -,s p ] / (, + 0 ) (2) %)E = [(,(d q + 0d p ) + 0 (s q +,s p )] / (, + 0) where %)W is the percentage change in wages in the relevant labor market, d q is the quantity shock to labor demand as a percentage of employment, d p is a wage subsidy given to employers as a percentage of the market wage, s q is the quantity shock to labor supply as a percentage of employment, s p is a wage subsidy given to workers as a percentage of the market wage,, is the elasticity of labor supply with respect to wages, 0 is -1 times the elasticity of labor demand with respect to wages (and hence is positive), and %)E is the percentage change in employment in the relevant labor market. In addition, changes in wages and employment in the shocked labor market would shift demand and supply in other labor markets. These shifts would change wages and employment in still other labor markets, leading to further shifts in supply and demand in all markets, until we reach a new general equilibrium. What do we know about labor demand and supply elasticities? We know a lot about aggregate labor demand elasticities, which will be relevant to the effects of shocks on overall wages and employment. Research suggests that in the short run, the elasticity of labor demand with respect to wages will be high, probably greater in absolute value than -3. 2 In the long run, the overall labor demand elasticity will be even greater, perhaps even infinite. 3 1 These are standard results in economics; see Freeman (1977) or Katz (1998). These equations can be derived by differentiating and rearranging the equilibrium condition L(W(1 + S p )) (1 + S q ) = E(W(1- D p )) (1 + D q ). L( ) is the labor supply function and E( ) is the employment demand function. The wage subsidies and quantity shocks are expressed as proportions of wages and employment. 2 Hamermesh s (1993) review says that the output-constant elasticity of labor demand is -0.3, but the relevant elasticity for analyzing effects of supply and demand shocks should allow output to vary. In this short run, this elasticity is 1 divided by the factor price elasticity for overall labor : how the wage employers are willing to pay varies with labor, holding capital constant. Hamermesh concludes that this factor price elasticity is -0.3, so the short-run demand elasticity for overall labor, allowing output to vary, is 1/(-0.3) = -3.33.

6 In contrast, we know little about the elasticity of demand for types of labor. 4 Regressions that use relative employment of labor types as a dependent variable find modest effects of relative wages on relative employment (Grant, 1979). Regressions that use relative wages of labor types as a dependent variable find modest effects of relative employment on relative wages, which suggests large elasticities of relative labor demand with respect to relative wages (Berger, 1983; Borjas, Freeman, and Katz, 1997). Either approach is unconvincing because both relative wages and relative employment are endogenous, biasing estimation. The most convincing evidence convincing because the right-hand-side variable is plausibly exogenous is from the minimum wage literature, which finds that minimum wages have modest effects, if any, on the relative employment of minimum wage workers such as teenagers. Traditionally, economists have believed that labor supply is unresponsive to wages. More recent estimates suggest larger labor supply elasticities for low-skilled groups, as high as 0.4 (Juhn, Murphy, and Topel, 1991). The effective labor supply elasticity will be even larger in models with involuntary unemployment. Unemployment can be included in models by assuming that wages are a function of unemployment (a wage curve ). Conditional on labor supply, the wage curve acts as an effective labor supply curve. Most estimates of wage curves suggest large labor supply elasticities, perhaps greater than 1. 5 Involuntary unemployment also complicates the wage and displacement effects of supply and demand shocks. The unemployment rate could affect labor supply or demand; labor market 3 An infinite labor demand elasticity is implied if production is constant returns to scale in labor and capital, and long-run capital supply is perfectly elastic. Suppose a supply shock lowers the wage. This increases profits, which increases capital supply, thus increasing output and labor demand and forcing the wage back up. If the profit rate is set by a long-run horizontal capital supply curve, then equilibrium will be restored at the original wage, implying a long-run horizontal labor demand curve. With constant returns, the wage and profit rate are functions of the capital labor ratio, so if the profit rate is the same, so must be the wage. 4 This agrees with Hamermesh (1993): Knowledge of the extent of substitution among various groups of workers is not well developed (p. 136). 5 Blanchflower and Oswald (1994) suggest the effect of ln(unemp. rate) on ln(wage) is -0.1. If unemployment is 6 percent, a 1 percent decrease in unemployment would increase wages by 1.6 percent. Crosssection studies suggest that a 1 percent decease in unemployment increases labor force participation by half a percent (Bowen and Finegan, 1969). Combining these relationships, a 1.5 percent increase in employment is associated with a 1.6 percent increase in wages.

7 conditions cannot be characterized solely by the wage rate. The direct effects of supply shocks on demand curves, or of demand shocks on supply curves, should be included in models. Therefore, we have little conclusive evidence on the magnitude of wage and displacement effects of supply or demand shocks. This paper s model provides a structure for thinking about these issues and presents new empirical evidence. 3. Description of Structural Model and Data The model is estimated using pooled time-series cross-section data. The model s observations are means or aggregates of labor market variables for a state/year cell. The data encompass all 50 states and the District of Columbia and all years from 1979 to 1997. The data come from the Outgoing Rotation Group of the Current Population Survey (CPS-ORG). The model s 23 equations are estimated using weighted least squares, with 1979 state population for weights. Fixed effects for state and year are included in all equations to reflect omitted characteristics of states or time periods. The model includes equations for five groups: female heads of household who are not college graduates and who have other relatives present in the household; 6 other women who are not college graduates; female college graduates; males who are not college graduates; and male college graduates. The model can be divided into five different sectors: six labor demand equations, one for each group and one overall; six wage equations; five labor force participation rate equations, one for each group; five population equations; and one equation explaining state personal income. The model s estimates are used to simulate the effects of labor supply shocks and demand shocks. The model includes unemployment, which makes it more realistic: we observe unemployment, and unemployment varies greatly over time, across different groups, and across different local markets. Empirical evidence shows that unemployment predicts wages. 7 6 This is the closest one can come to consistently defining single mothers using CPS-ORG data. 7 Unemployment predicts wages better than employment/population ratios, which would fit a marketclearing model (Blanchflower and Oswald, 1994).

8 The model is estimated using local data, not national data. Using local data provides more observations, allowing more precise estimates. In addition, empirical evidence suggests that labor market outcomes are more influenced by local variables than national variables (Blanchflower and Oswald, 1994; Bartik, 1994). State data are used rather than metropolitan data, even though metropolitan areas are closer to true local labor markets. States are chosen for data reasons. Metropolitan area boundaries change greatly over time, making it difficult to define consistent variables. In addition, sampling for the CPS is designed to produce reliable estimates at the state level (for example, by oversampling smaller states) but is not designed for reliable estimates for smaller metropolitan areas. The model identifies cause and effect relationships by lagging right-hand-side variables and including lagged dependent variables as controls. We would like to allow right-hand-side variables to have immediate effects. However, almost all the right-hand-side variables are endogenous, and it is difficult to find good instruments for so many endogenous variables. The identifying assumption that labor market behavior responds to other variables with a lag seems plausible. Including lagged dependent variables allows the dynamic behavior of the model to be more complex. Lagged dependent variables also control for recent state trends. Controlling for such unobserved trends, the estimated effects of other variables on the dependent variable is more likely to represent a true causal influence. Table 1 summarizes the model. The demand equations impose the restrictions that overall labor demand depends on average wages and that relative demand for each type of labor depends on each type s relative wage. This specification can be derived from a production function in which labor enters in aggregate form, with that labor aggregate produced by a subproduction function that is constant-elasticity-of-substitution in the five labor types. Less restrictive specifications, in which demand for each labor type depends on all five wages, resulted in estimates that were too imprecise.

9 Table 1. Summary of a Wage Curve Model of State Labor Markets Type of Equation Overall labor demand (1 equation) Employment share demand (5 equations) Overall wage curve (1 equation) Relative wage curves (5 equations) Labor force participation rate (5 equations) Migration (5 equations) Income (1 equation) Dependent Variable ln(state employment) ln(share of employment in group) ln(wage) ln(wage of group/overall wage) ln(labor force participation rate of group) ln(population of group) ln(state personal income) Independent Variables (in addition to year and state dummies, and two lags of dependent variable). All dependent variables are included with two lags and no current values unless otherwise noted. ln(wage) ln(personal income) ln(wage of group/overall wage) current value of ln(labor force share of group) [endogenous, lagged labor force share used as instrument] ln(unemployment rate) Some function of relative unemployment of group, with functional form chosen for each group after preliminary testing ln(wage of group) unemployment rate of group ln(afdc benefits for female head group) Same as for labor force participation ln(wage) ln(employment) ln(population) Includes current as well as lagged values of these variables Notes: All estimates based on pooled annual time-series cross-section data for all states, 1979-97. All estimates are weighted by 1979 state population. All estimates use weighted least squares except employment share demand, which is weighted 2SLS. Employers with a job opening may base hiring in part on who is in the labor queue, not just on wages. To allow for this, the equations for the relative labor demand for each group also include the labor force share of each group. The current values of labor force share are included, because hiring should depend on the current labor queue. Because measurement error in labor force share will be correlated with measurement error in employment share (both variables are measured using the CPS-ORG data), lagged labor force share is used as an instrument for current labor force share.

10 The overall wage curve in the model is standard, but it implicitly assumes that overall wages depend on overall unemployment and not on relative unemployment of different groups. The relative wage equations assume the relative wage is affected by relative unemployment. Less restrictive specifications, in which each group s wage rate depends on all the group s unemployment, were too imprecise. Some experimentation was done with the functional form by which unemployment affects wages. For each wage curve, four different specifications were estimated, each with a different functional form for unemployment: linear; unemployment and unemployment squared; the natural logarithm of the unemployment rate; and one over the unemployment rate. The specification that minimizes the Akaike Information Criterion was chosen for use in simulations. The labor force participation equations and migration (or population) equations are standard. An income equation is included, and income is included in the labor demand equation, to allow for multiplier effects. As state employment increases, income increases, increasing local output demand, which will further increase local labor demand. The income equation includes current right-hand-side variables because income will increase immediately if wages, employment, and population in the state increase. The system is still identified because income enters with a lag in the overall labor demand equation. The equation system seems sparse because only a few continuous variables are included in each equation. Including state and year dummies means that the model does control for many variables. The state dummies control for variables that vary among states but not much over time. The year dummies control for variables that change over time in a similar manner for different states. The model is estimated using weighted least squares, with 1979 state population as weights. Using state population as weights increases the precision of estimates, because CPS- ORG samples are larger for the larger states. State population weights also mean that the estimates describe the behavior of the average state, where average reflects the relative

11 population in each state. State population from 1979 is used as weights, rather than population for each state/year cell, to ensure that the weighting variable is not endogenous. 8 These estimated equations are used to simulate the impact of various shocks to the labor supply or demand of different groups. Appendix 1 gives an example of the simulation program. The wage curve equations are nonlinear, and so the model requires assumptions about the baseline unemployment rate. With lower unemployment, wages respond more to shocks, which affects other variables. The simulations consider both low-unemployment and highunemployment baselines. For the low-unemployment baseline, unemployment rates for each group are taken from national averages for the lowest unemployment year (1997) in the sample; for the high-unemployment baseline, unemployment rates are from the highest unemployment sample year (1982). This paper focuses on national effects of labor supply or demand shocks, that is, the average effects in all states of labor supply or demand shocks that take place in all states. Such an analysis should incorporate spillover effects across states. I explored modeling spillover by adding national variables to the equations, which requires changing from fixed to random year effects, but in most cases the national variables had counter-intuitive signs. This may reflect the limited number of available national observations (18 years). To estimate national effects, most simulations suppress the migration effects of supply or demand shocks. This approach will approximate national effects of a shock if migration is the main spillover effect across states. The assumption is that if a shock takes place in all states, the resulting adjustments should not involve significant migration. All simulations also were done with migration effects allowed. The difference in estimations with and without migration are slight, reflecting the modest effects of wages and unemployment on migration. 8 Because all equations include a state fixed effect, state population from any year can be used as a weight without bias, as long as the weight does not vary across years for a state.

Table 2. 1997 National Means of Labor Market Outcomes for Five Demographic Groups and Overall Population Ages 16-64 Female Male Household Heads; Ages 16-44; Other relatives present, Less than college ed. Ages 16-64; Less than college ed.; except for first group College graduates; Ages 16-64 Less than college ed.; Ages 16-64 College graduates; Ages 16-64 Overall Population; Ages 16-64 Proportion of population 0.0399 0.3569 0.1091 0.3782 0.1159 1.0000 Wage rate $8.49 $8.80 $15.19 $10.85 $18.85 $11.29 Unemployment rate (1982 rate in parentheses) 11.0 (15.4) 5.4 (10.2) 2.2 (4.2) 6.0 (12.0) 1.9 (3.1) 5.0 (9.9) Labor force participation rate 75.7 66.5 82.8 81.5 93.1 77.4 Notes: All data are taken from 1997 Merged Outgoing Rotation Group data tape of the Current Population Survey, with the exception of the unemployment rate data for 1982. All means are weighted national means using appropriate weights from tape. Mean wage rate is actually exp(mean ln(hourly wage)). Over sample period of 1979-97, 1997 is year with lowest national unemployment rate for 16-64 year olds, and 1982 is year with highest national unemployment rate. In this paper, the patterns of unemployment in these two years are used as alternative baselines in simulating the effects of supply and demand shocks.

13 Table 2 summarizes the means of some variables for the five groups. The means have the pattern one would expect, with less-educated groups having lower wages, lower labor force participation, and higher unemployment rates than more-educated groups, and women having lower wages and labor force participation rates than men. 4. Estimation Results: Elasticities Implied by the Model In this section, I present the implications of the model s estimates for the elasticities of labor demand, supply, and other labor market behavior. 9 The model s elasticity of overall labor demand with respect to wages is summarized in Figure 2. 10 The figure shows the elasticity both with income held fixed and with income allowed to vary. The estimates here of income-constant elasticities (of -0.2 or -0.4 in the short run, and -0.8 after eight years or so) are consistent with estimates of output-constant labor demand elasticities in the literature (Hamermesh, 1993). When personal income is allowed to vary, the model implies that labor demand elasticities with respect to wages head off towards infinity in the very long run, which is consistent with the theory of section 2. A wage decrease increases employment, which increases income, which further increases employment, and the process continues. As explored in sections 2 and 5, a flat long-run demand curve implies that supply shocks have small long-run displacement effects on the overall labor market, while demand shocks have large long-run displacement effects on the overall labor market. Estimates of relative labor demand elasticities for labor types with respect to relative wages are shown in Figure 3. Estimates of relative demand elasticities are modest, about 0.1 in 9 Appendix 2 presents parameter estimates for the 23 model equations. The parameter estimates are relegated to the appendix because they are not readily interpretable. 10 Estimates in figures and tables are based on 1000 Monte Carlo repeated simulations of the model, with each simulation based on one random draw from the distribution of parameter estimates for the 23 estimated equations. These 1000 Monte Carlo repetitions are used to generate average elasticities and effects, standard errors of such effects (the standard deviation of the effect in the 1000 repetitions), and pseudo t-statistics for the effects (the ratio of the average effects to the standard deviation of the effects. This approach is used because of the difficulty in generating analytical standard errors in this complicated non-linear model.

14 Figure 2. (-1) Times Elasticity of Overall Employment Demand With Respect to Overall Wages, With and Without Income Varying Elasticity 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0-0.2 0 1 2 3 4 5 6 7 8 9 10 Years After Shock VARY NOVARY 5 years 10 years Income not allowed to vary 0.717 (11.22) 0.808 (12.43) Income allowed to vary 0.722 (5.84) 1.431 (4.48) Notes: Pseudo t-statistics, derived from 1000 Monte Carlo repetitions of simulations, are in parentheses. Elasticities derived from decreasing overall wages by 10 percent. Simulation with income varying also allows income equation in model to become operational, with feedback between labor demand and income equations. absolute value after five years for most groups. These estimates are consistent with the minimum-wage literature (Katz, 1998). Estimates of how relative labor demand responds to relative labor supply, holding relative wages constant, are presented in Table 3. These effects of relative labor supply are large, consistent with the argument in section 3 that who employers hire depends on who is in the queue.

15 Figure 3. Elasticity of Group-Specific Labor Demand Relative To Overall Labor Demand Where Income is Not Allowed to Adjust Elasticity 0.15 0.1 0.05 0 FHEAD LEF MEF LEM MEM -0.05-0.1 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Group Female Heads of Household Other Less-Educated Females More-Educated Females More-Educated Males 5-year elasticity 0.122 (1.29) 0.067 (4.24) -0.019 (0.26) 0.096 (3.58) 0.068 (1.79) Notes: Pseudo t-statistics are in parentheses, derived from 1000 Monte Carlo repetitions of effects of shock. Effects are 1(elasticity of ln(employment in group/employment overall)) with respect to ln(wage of group/overall wage). Elasticities are derived from decreasing wage of group by 0.10, with resulting effects multiplied by 10 to generate the table and figure.

16 Table 3. Estimates of Sensitivity of Relative Labor Demand to Relative Labor Supply, Holding Relative Wages Constant Group Short-Run (Immediate) Elasticity Implied Long-Run Elasticity Female heads of household 0.375 (1.56) Other less-educated females 0.850 (14.00) More-educated females 0.301 (1.96) Less-educated males 0.428 (3.44) More-educated males 0.401 (3.98) 0.486 0.919 0.451 0.680 0.588 Notes: Effects are derived directly from parameter estimates in relative labor demand elasticities. See Appendix 2 for complete set of estimates. Short-run effect is from equation explaining ln(employment share of group) and is coefficient on ln(labor force share of group). t-statistic is in parentheses. Long-run effect is this short-run effect divided by (1 minus (sum of coefficients on two lagged dependent variables in equation)). Estimates of elasticities of labor supply of different groups with respect to wages or unemployment are presented in Table 4. Wages are estimated to have little effect on labor supply, with the exception of modest effects on the migration of male and female college graduates. This is consistent with most previous research. Unemployment rates have large effects on both labor force participation and migration. The effects on labor force participation and population migration are consistent with previous research (Bowen and Finegan, 1969; Herzog and Schlottmann, 1993).

17 Table 4. Summary of Medium Run Elasticities of Labor Supply With Respect to Wages and Unemployment Heads of Household Females Other Less-educated Males Moreeducated Lesseducated Moreeducated All Five Groups Wage elasticities after 5 years Labor Force Participation Rate 0.098 (1.38) -0.025 (0.51) -0.057 (1.89) 0.030 (1.64) 0.024 (1.58) 0.021 (1.05) Population -0.140 (1.06) -0.039 (0.45) 0.236 (2.24) 0.012 (0.15) 0.397 (3.29) 0.048 (0.98) Total Labor Force -0.042 (0.28) -0.064 (0.66) 0.178 (1.63) 0.042 (0.49) 0.421 (3.44) 0.069 (1.33) -1 times Unemployment Elasticities after 5 years Labor Force Participation Rate 0.298 (3.18) 0.661 (5.15) 0.149 (1.07) 0.374 (8.02) 0.173 (2.04) 0.492 (8.92) Population 0.121 (0.66) 0.262 (1.17) 0.447 (0.89) 0.508 (2.60) 2.769 (3.83) 0.632 (4.25) Total Labor Force 0.420 (1.98) 0.923 (3.60) 0.596 (1.14) 0.882 (4.33) 2.943 (4.05) 1.124 (6.93) Notes: Estimates are derived from 1000 Monte Carlo repetitions of two different simulations: one where all ln(wages) are increased by 0.10, the other where all unemployment rates are reduced by 0.01. Elasticities are change in natural logarithm of the three labor force variables, divided by change in the wage or unemployment rate variable, and, for unemployment, multiplied by -1. Absolute values of pseudo t-statistics are in parentheses below elasticity estimates, and is equal to absolute value of mean elasticity from 1000 repetitions divided by standard deviation of elasticity in 1000 repetitions. Estimates are elasticities after five years; elasticities only slowly change after five years. For example, elasticity of total overall labor force after 10 years with respect to wages is 0.039 (0.52=t), from 0.069 (t=1.33) after 5 years. Elasticity of overall total labor force after 10 years with respect to unemployment is 1.408 (t=6.15), compared to 1.124 (t=6.93) after 5 years. As Figure 4 shows, reductions in unemployment have large effects on wages. These effects on wages gradually unfold, so that the wage inflation rate is higher for a while after an unemployment reduction, resulting in a short-run Phillips curve. The nonlinearity of the wage curve implies that if unemployment is initially lower, a reduction in unemployment has effects on wages that are greater.

18 Figure 4. Elasticity of Overall Wages With Respect to Unemployment Under Conditions of High and Low Initial Unemployment 6 5 LOW HIGH 4 Elasticty 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Elasticity of Wages With Respect to 1% Reduction in Unemployment After 5 years After 10 years Low Unemployment at Baseline 3.317 (15.13) 4.959 (12.40) High Unemployment at Baseline 1.629 (15.13) 2.435 (12.40) Notes: Results are change in ln(wage) multiplied by 100, for 1% reduction in unemployment of all five groups. Base unemployment rates in low-unemployment baseline are actual national unemployment rates for five groups in 1997. For high-unemployment baseline, actual national unemployment rates for five groups as of 1982 were used. 1982 and 1997 were highest and lowest unemployment years in nation from 1979-97. See Table 2 for actual values of unemployment rates for each group in 1982 and 1997. Figure 5 shows that a change in unemployment of one group has effects on relative wages that are small, regardless of the initial unemployment rate. A 1 percent unemployment reduction for a group increases the group s relative wage by less than one-third of 1 percent after

19 Figure 5. Group-Specific Elasticity With Respect to Unemployment for Group-Specific Wages Relative to Overall Wages Under Conditions of Low Initial Unemployment 0.4 0.35 0.3 0.25 FHEAD LEF MEF LEM MEM Elasticity 0.2 0.15 0.1 0.05 0-0.05 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Low- Unemployment Baseline High- Unemployment Baseline Female Heads of Household 0.085 (3.70) 0.047 (3.84) Other Less-educated Females 0.341 (3.02) 0.142 (3.86) More-educated Females 0.287 (2.97) 0.273 (2.83) Less-educated Males 0.236 (3.70) 0.173 (3.18) More-educated Males 0.342 (2.27) 0.322 (2.15) Notes: Pseudo t-statistics are in parentheses, derived from 1000 Monte Carlo repetitions of simulation. Simulation shows effect on 100 times ln(wage of group/average overall wage) of reduction of 1% in unemployment of that group, with unemployment rates for other groups staying unchanged. five years. Effects of overall unemployment on overall wages are five to ten times as great. The estimates are consistent with labor market institutions and customs that resist changes in relative wages.

20 The estimated wage curves, and the effects of unemployment on labor force participation and migration, imply that the model s effective labor supply elasticity with respect to wages is much greater than Table 4 s tiny wage elasticities of labor supply. An effective labor supply elasticity can be calculated by estimating the effect of a demand-induced change in unemployment on employment and wages. The ratio of the percentage change in employment to the percentage change in wages from this exercise is an effective labor supply elasticity. Effective labor supply elasticities are shown in Figure 6. These supply elasticities are large, particularly in the short run. In a wage curve model, short-run elasticities are large because employment adjusts faster than wages. Elasticities decline over time as wages adjust, although long-run elasticities are still higher than the conventional wisdom in economics. Effective supply elasticities are higher if population as well as labor force participation is allowed to adjust. Effective supply elasticities are also higher if initial unemployment is higher, because wages are less sensitive to increased demand when unemployment is high. 5. Empirical Estimates: The Effects of Demand and Supply Shocks In this section, I present simulations of the effects of shocks to the quantity supplied or demanded of some labor type. I first consider shocks to the quantity of labor supplied of some type of labor. Such shocks could be brought about by welfare-to-work programs. Figure 7A shows the effects on the overall labor market of an increase in the labor supply of female household heads. As shown in the table below the figure, a given percentage change in overall labor supply results in effects on overall employment and wages of virtually the same magnitude, regardless of which group s labor supply is shocked. An increase in labor supply results in some initial displacement, as wages and employment only gradually adjust to the labor supply shock. Even in the medium run (five years), the supply shock results in displacement and wage declines. Eventually, employment adjusts upwards to the expanded labor supply, and

21 Figure 6. Complete Labor Supply Elasticities With and Without Population Adjustment Under Conditions of High (Bold Lines) and Low (Regular Lines) Initial Unemployment Elasticity 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 POPH NOPOPH POPL NOPOPL 0 1 2 3 4 5 6 7 8 9 10 Year After Shock Low Initial UR, No Population Adjustment Allowed Low Initial UR, With Population Adjustment High Initial UR, No Population Adjustment Allowed High Initial UR, With Population Adjustment Effective Labor Supply Elasticity After 5 Years 0.473 (12.71) 0.725 (10.14) 0.912 (12.94) 1.351 (10.12) Notes: These numbers are derived from simulation that specified exogenous 1% reduction in unemployment rate for all groups, and used wage curve equations, labor force participation rate equations, and population migration equations to simulate effects of this change on wages and the labor force. The effective labor supply elasticity is the ratio of the change in the natural logarithm of the overall labor force to the change in the average log wage. Pseudo t-statistics from 1000 Monte Carlo repetitions of simulation are in parentheses. Low initial unemployment rates are national unemployment rates of 1997 (overall average = 5.0%), high initial unemployment rates are national unemployment rates of 1982 (overall average = 9.9%).

22 Figure 7A. Overall Elasticity of Wages, Employment and Total Labor Supply and the Displacement Rate from a Supply Shock to Female Heads With Low Initial Unemployment 2.5 2 1.5 Elasticity 1 0.5 0-0.5-1 -1.5-2 Wage Emp Labor Disp -2.5-1 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Elasticities after five years: Elasticity (pseudo t-statistic) Labor Supply Employment Wage Displacement 0.788 (15.87) 0.660 (4.11) -2.086 (10.97) 0.284 (1.63) Notes: Elasticities come from supply shock to female heads that is equal to 0.001 of overall population. Elasticities calculated by dividing change after five years in ln of overall labor supply, employment, or wage, by original change in ln of overall labor supply. Displacement is equal to 1-(change in overall employment divided by change in employment of those added to labor force by labor supply shock). Pseudo t-statistics are derived by 1000 Monte Carlo repetitions of simulation. Labor supply elasticities in figure are significant from year 0 to year 10, employment elasticities are significant from year 4 on, wage elasticities are significant from year 1 through year 8, and displacement elasticities are significant from year 0 through year 5, and again in years 8 through 10. Numbers for elasticities are quite similar if do other four groups, which give rise to following estimates: Less-educated Females More-educated Females Less-educated Males More-educated Males Labor Supply Employment Wage Displacement 0.723 (17.10) 0.852 (10.58) 0.748 (20.73) 0.803 (17.09) 0.648 (4.15) 0.654 (4.04) 0.660 (4.14) 0.665 (4.07) -1.966 (11.22) -2.185 (9.40) -2.018 (11.89) -2.128 (11.37) 0.350 (2.23) 0.361 (2.28) 0.333 (2.07) 0.354 (2.23)

23 Numbers are also not much different if allow population to adjust. Same overall elasticities, calculated based on shock to female heads, in case where population adjusts, are given by 5-year Elasticity When Population is Allowed to Adjust Labor Supply Employment Wage Displacement 0.711 (7.24) 0.683 (4.76) -1.702 (6.47) 0.260 (1.67) As can be seen in this table, with population migration, there is some reduction in the labor supply effects of the shock due to out-migration, which moderates the wage effects of the shock somewhat. In the above tables, pseudo t-statistics are calculated based on 1000 Monte Carlo repetitions. Calculated t-statistics for displacement assume denominator of ratio used in calculation is nonstochastic; checks in a few cases indicate that changing this assumption makes no difference in calculated t-statistic, as employment change in group added to labor supply is largely non-stochastic, with very small variance because most of change is assumed. supply shock. Even in the medium run (five years), the supply shock results in displacement and wage declines. Eventually, employment adjusts upwards to the expanded labor supply, and wages come back to their original level. However, this adjustment to the shock takes at least seven to ten years. If the initial unemployment level is high, this adjustment to the labor supply increase is even more protracted. With high unemployment (Figure 7B), wages initially respond less to the supply shock, which thereby delays the employment response to the supply shock. How does a shock to some group s labor supply affect that group s labor market? 11 As Figure 8 and the accompanying table show, the effects on the group s relative wages are slight, reflecting the resistence of relative wages to change in this model. But as Figure 9 and the accompanying table show, the effects on the group s relative employment are large. However, effects on the group s employment are still not large enough to avoid unemployment and displacement effects on the group that are sizable and persistent. For example, after five years the percentage increase in employment in usually only about half the percentage shock to labor supply, which implies that about half the shock results in displacement and unemployment. For some of the smaller groups, unemployment and displacement persist even after ten years. The 11 Groups other than those shocked all have similar percentage wage effects and employment effects, which are quite similar to the effects on overall wages and employment.

24 Figure 7B. Overall Elasticity of Wages, Employment and Total Labor Supply and the Displacement Rate from a Supply Shock to Female Heads With High Initial Unemployment 2.5 2 Elasticity 1.5 1 0.5 0-0.5-1 -1.5-2 Wage Emp Labor Disp -2.5-1 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Elasticities after five years: Labor Supply Employment Wage Displacement Elasticity (pseudo t-statistic) 0.763 (17.82) 0.356 (4.07) -1.190 (12.61) 0.614 (6.48) Notes: Elasticities come from supply shock to female heads that is equal to 0.001 of overall population. Elasticities calculated by dividing change after five years in ln of overall labor supply, employment, or wage, by original change in ln of overall labor supply. Displacement is equal to 1-(change in overall employment divided by change in employment of those added to labor force by labor supply shock). Pseudo t-statistics are derived by 1000 Monte Carlo repetitions of simulation. Labor supply elasticities in figure are significant from year 0 to year 10, employment elasticities are significant from year 4 on, wage elasticities are significant from year 1 through year 10, and displacement elasticities are significant from year 0 through year 6. Elasticities are quite similar for shocks to other four groups, which give rise to following estimates: Labor Supply Employment Wage Displacement Less-educated females 0.696 (20.00) 0.349 (4.12) -1.124 (13.01) 0.648 (7.57) More-educated females 0.822 (10.55) 0.353 (4.01) -1.238 (10.30) 0.665 (7.96) Less-educated males 0.724 (28.13) 0.356 (4.11) -1.155 (13.96) 0.634 (7.11) More educated males 0.770 (19.38) 0.358 (4.04) -1.205 (12.76) 0.665 (8.01)

25 Numbers are also not much different if allow population to adjust. Same overall elasticities, calculated based on shock to female heads, in case where population adjusts, are given by: 5-year Elasticity When Population is Allowed to Adjust Labor Supply Employment Wages Displacement 0.679 (7.94) 0.389 (4.62) -1.010 (7.36) 0.578 (6.33) As can be seen in this table, with population migration, there is some reduction in the labor supply effects of the shock due to out-migration, which moderates the wage effects of the labor supply shock somewhat. In above tables, pseudo t-statistics are calculated based on 1000 Monte Carlo repetitions. Calculated t-statistics for displacement assume denominator of ratio used in calculation is nonstochastic; checks in a few cases indicate that changing this assumption makes no different in calculated t-statistic, as employment change in group added to labor supply is largely non-stochastic, with very small variance because most of change is assumed. two largest groups (less educated men and other less-educated women) show full employment adjustment to a supply shock to that group after ten years. A shock to a group s labor supply expands the entire local economy, and groups that are a larger proportion of the labor force naturally share more of the expanded employment that results. To dramatize how labor supply shocks differentially affect various groups, consider the employment effects after 10 years of an increased labor supply of female household heads. As shown in Table 5, with initially low unemployment, for every 100 persons added to the labor force by this shock, roughly 88 are expected to be employed at the end of 10 years. These 88 displace some female heads from employment, reducing employment by about 46 among other female heads. Net employment of female heads goes up by about 42 (88-46). But as a result of the expansion of the economy brought about by adding more female heads to the labor supply, more individuals in the long run are employed in all other groups. Overall, about 189 additional individuals are employed, which implies that about 147 non female heads are employed because of the shock (147 = 189-88 + 46). The net employment effects on female heads are considerably greater in percentage terms, however, as female heads are only 4 percent of the working-age population.

26 Figure 8. Elasticity of Group-Specific Wages With Respect to Initial Labor Force Shock to That Group With Low Initial Unemployment Elasticity 0.2 0.1 0-0.1-0.2-0.3-0.4-0.5-0.6-0.7-0.8-0.9-1 -1.1-1.2-1 0 1 2 3 4 5 6 7 8 9 10 Years After Shock FHEAD LEF MEF LEM MEM Female Heads of Household Less-educated Females More-educated Females Less-educated Males More-educated Males Elasticity With Low Initial Unemployment -0.105 [-3.003] {-2.086} (5.61) -0.672 [-2.089] {-1.966} (11.72) -0.354 [-3.780] {-2.185} (4.40) -0.914 [-2.166] {-2.018} (12.16) -0.410 [-3.143] {-2.128} Elasticity With High Initial Unemployment -0.061 [-1.748] {-1.190} (5.69) -0.381 [-1.184] {-1.124} (13.40) -0.260 [-2.782] {-1.238} (3.50) -0.540 [-1.279] {-1.155} (13.49) -0.286 [-2.193] {-1.205} (4.15) (5.67) Notes: First number in each box are elasticities after five years, calculated as estimated change after five years in ln(wage of group) divided by initial change in ln(labor force of same group). Number in brackets [ ] below is elasticity calculated by dividing change after five years in ln(wage of group), divided by initial change in ln(overall labor force). Number in braces { } to right is elasticity of overall wages, calculated relative to initial change in overall labor force. These overall elasticities are the same ones reported in tables below Figures 7A and 7B. Elasticities are calculated from simulations of labor supply shock of 1% of overall population. Simulations are for model with migration suppressed. Pseudo t-statistics from 1000 Monte Carlo repetitions of simulation are reported in parentheses. Figure presents effects with low base unemployment rates. Wage effects with low unemployment rate are statistically significant from 1-9 years after shock for female heads, more-educated females, and moreeducated males, and from 1-8 years after shock for less-educated females and less-educated males. With high unemployment, all wage effects are statistically significant from 1-10 years after shock.

27 Figure 9. Own Group Employment Elasticity for a Supply Shock With Low Base Unemployment and No Population Adjustment 1.40 1.20 1.00 FH LEF MEF LEM MEM Elasticity 0.80 0.60 0.40 0.20 0.00 0 1 2 3 4 5 6 7 8 9 10 Years After Shock Female Heads Less-educated Females More-educated Females Less-educated Males More-educated Males Elasticity With Low Initial Unemployment 0.424 [12.128] {0.660} (1.75) (4.11) 0.690 [2.144] {0.648} (10.56) (4.15) 0.454 [4.847] {0.654} (2.77) (4.04) 0.661 [1.568] {0.660} (8.04) (4.14) 0.588 [4.504] {0.665} (6.72) (4.07) Elasticity With High Initial Unemployment 0.413 [11.817] {0.356} (1.69) (4.07) 0.585 [1.818] {0.349} (12.65) (4.12) 0.424 [4.527] {0.353} (2.62) (4.01) 0.539 [1.276] {0.356} (8.75) (4.11) 0.547 [4.192] {0.358} (6.37) (4.04) Notes: First number in each cell is employment elasticity for the group after five years, defined as estimated change after five years in ln(employment) of group, divided by initial change in ln(labor force of same group). Number in brackets [ ] below is elasticity relative to initial change in ln(overall labor force). Number in braces { } to right is elasticity of overall employment with respect to initial change in ln(overall labor force). This is included to allow for examination of effects of shocks on relative employment. Numbers in parentheses below are pseudo t-statistics, derived by dividing estimate by standard deviation of estimates in 1000 Monte Carlo repetitions of simulation. Elasticities are calculated from simulations of labor supply shock of 0.1% of overall population. Ten different simulations are reported in table, with five different shocks considered (one for each group), under two initial unemployment conditions, low and high unemployment. Simulations are for models with migration suppressed. Employment elasticities are significant at 95% confidence level for all groups except female heads, for whom pseudo t-statistics tend to be in 1.6-2.0 range for all 10 years after the shock.